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Main MenuDisc 4 Table of ContentsHelpSearchStability Analysis: Where Do We Stand?l C. S. Lin, M. R. Binns, and L. P. Lefkovitch2 ABSTRACT To clarify the apparent confusion arising from the diversity of published stability statistics, and the relationship of these with the clustering of genotypes for similarity of response to environments, the interrelationship of nine stability statistics and nine similarity measures are investigated. The stability statistics fall into four groups depending on whether they are based on the deviations from the average genotype effect or on the genotype X environment (GE) term, and whether or not they incorporate a regression model on an environmental index. These groups of stability statistics are shown to be related to three concepts: A genotype may be considered to be stable (i) if its among-environment variance is small, (ii) if its re- sponse to environments is parallel to the mean response of all geno- types in the trial, or (iii) if the residual mean square from a regression model on the environmental index is small. Unfortunately, these three concepts represent different aspects of stability and do not always provide a complete picture of the response. In the alternative approach of cluster analysis, the similarity measures define complete similarity in three different ways: i) equality of genotype’s response across locations, ii) equality of all within location differences, and iii) equality of all within location ratios. The advantage of the non- parametric approach is that a cultivar’s response characteristics can be assessed qualitatively, without the need for a mathematical char- acterization. Additionul index words: Genotype X environment interaction, Cluster analysis, Cultivar assessment, Stability parameter. NCREASED concern with the importance of homeo- I stasis in living organisms has stimulated plant breeders’ awareness for the need to develop well-buff- ered cultivars. This has led to a greater emphasis on phenotypic stability in breeding programs. However, the concept of stability is by no means unambiguous; it is defined in many ways depending on how the sci- entist wishes to look at the problem, while the statistics that parameterize these various concepts are also nu- merous. This leads many scientists to wonder which stability statistics should be used for their particular problem. Empirical comparisons of several methods have been reported (e.g., Gray, 1982; Kang and Miller, 1984; Ntare and Aken’Ova, 1985). Although such studies provide interesting information, the relation- ships among the methods can be explicitly explored only if comparisons are based on the structure of the stability statistics themselves. Several authors (e.g., Easton and Clements, 1973) have attempted to do this, but without identifying the basic structures from which the methods were derived. The purpose of the present paper is to examine nine stability statistics currently in use, to show that they are derived from two components of a two-way clas- sification of the data, and that there are three types of stability concepts. These concepts are discussed both from statistical and biological points of view. Some limitations of the parametric approach to stability are noted, and as an alternative, a nonparametric ap- proach, namely to group genotypes according to their ’ Contribution no. 1-770 from the Engineering and Statistical Res. Centre, Res. Branch, Agric. Canada, Ottawa, Canada, KIA OC6 Re- ceived 14 Nov, 1985. - Research scientists, Engineering and Statistical Res. Centre, Agric. Canada. similarity of response to a range of environments, is discussed. Several published similarity coefficients used in cluster analyses are summarized and their interre- lationships are investigated. STABILITY STATISTICS For convenience, a two-way model is assumed. Let x,, represent the observed mean value of genotype i (i = 1, . . ., p) in environment j (j = 1, . . ., q), and let X, , X,,. and X denote the marginal means of genotype i, environment j, and the overall mean, respectively. The nine stability statistics most frequently cited are given, with their formulae, in Table 1; a brief descrip- tion of each follows. (1) The variance of a genotype across environments (q), can be a measure of stability. (2) Coefficient of variability (CV,). Francis and Kan- nenberg (1978) used the conventional CV% of each genotype as a stability measure. (3) Plaisted and Peterson’s (1959) mean variance component for painvise GE interaction (8,). The mean of the estimated variance components of the GE in- teraction for all pairs of genotypes that include geno- type i is the stability measure for genotype i. (4) Plaisted‘s (1960) variance component for GE in- teraction (t+,J. One genotype (i) is deleted from the entire set of data and the GE interaction variance from this subset is the stability index for genotype i. (5) Wricke’s (1962) ecovalence (q). The GE inter- action effects for genotype i, squared and summed across all environments, is the stability measure for genotype i. (6) Shukla’s (1972a) stability variance (uf). Based on the residuals in a two-way classification, the variance of a genotype across environments is the stability mea- sure. (7) Finlay and Wilkinson’s (1 963) regression coef- ficient (b,). The observed values are regressed on en- vironmental indices defined as the difference between the marginal mean of the environments and the over- all mean. The regression coefficient for each genotype is then taken as its stability parameter. (8) Perkins and Jinks’ (1968) regression coefficient (/3,). Similar to (7) except that the observed values are adjusted for location effects before the regression. (9) Eberhart and Russell’s (1 966) deviation param- eter (sf). The residual mean square (MS) of deviation from the regression defined in (7) or (8) is the measure of stability for each genotype. Other published stability statistics include Hanson’s (1 970) relative and comparative genetic stabilities, which will be considered in connection with clustering methods, and Tai’s (1971) a, and A,, which can be regarded as a special form of that of Eberhart and Russell (1 966), when the environmental index is as- sumed to be random. Note that Plaisted and Peterson’s (1959), and Pla- isted’s (1 960) statistics were originally defined in terms of replicated data, while in

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